The thought is appealing. However, such a thought would be assuming that the characteristics of all pigments are the same and that using the same oil with each pigment would produce the same results.

Keep in mind: it is important that the properties of the oil are adapted to the characteristics of the pigment.

If grinding an earth color with linseed oil is an excellent formula, why is it not an excellent formula to grind a white or even a blue pigment with that same oil?
Linseed oil has some great qualities, but if it is used to excess, the oil dries like the skin of an orange or even in wrinkles, and moreover, adhering to the standard conservation rule of keeping a painting out of direct sunlight, linseed oil yellows.
Regarding brown pigments, the yellowing is imperceptible, but for white or blue pigments, the color harmony of the painting can completely change over time. Think of the paintings of the Romantic Dutch School.

Sometimes it is not just the yellowing of the pigments that one must consider.
The creaminess of the paint is essential for the artist's work, but some pigments ground with linseed oil are very structured, mix much more easily, and are more workable longer if ground with poppy seed oil. Is this not the specificity of oil paint?
The workability of the paste is altogether different, enabling it to be mixed directly on the canvas with the greatest facility.

Some authorities maintain that Monet achieved successful results painting water lilies thanks to the use of poppy seed oil.

In the past, the use of walnut oil with pigments has also given good results.
Other oils such as safflower or sunflower oil are now used by certain manufacturers, but in the category of non-yellowing oils, poppy seed oil still gives the best results.
Moreover, poppy seed oil is often added to improve other oils, but in small quantities due to its high price.

We believe that even if different oils could mix together without problems, it is preferable to grind pigments in a single oil only. In this way, the best results are obtained.

Our colors are therefore ground with oil that produces the best results – be that only with linseed oil or only with poppy seed oil.

On canvas, the colors can be mixed without any problems and will keep their specific qualities wherever they are applied unmixed. We have more than 135 years experience on this subject.

The oil paints used straight from the tube without the admixture of a medium do not need to be varnished.

The blues will stay blue, the whites will stay white, and the freshness of the tints will be evident for a long time, a very long time.